Talk:Point groups in four dimensions

Scope of the article
There are several complete classifications of these point groups, most recently in Conway and Smith's book.

Most of the article is only about a subset of these groups, the ones generated by reflections and their subgroups (these are the ones for which Coxeter notation is appropriate), or the crystallographic point groups. This is nowhere indicated. For example ±[I×O], the very first one in Conway and Smith's list, is completely absent.

Maybe this article is about something else, and that should be a separate article?--GuenterRote (talk) 05:14, 27 December 2020 (UTC)


 * If this article is only about a subset of these groups, then where is the complete list? I see no reason not to include one. If Coxeter notation is not always applicable then use a different notation. Shadi1089 (talk) 20:30, 17 March 2021 (UTC)
 * That doesn't necessarily seem to be the best strategy, in my opinion.
 * For instance, it is often very convenient to denote points of the plane R2 as complex numbers. Although this is something that cannot be done for all dimensions of Euclidean space, that does not seem to be sufficient reason to stop doing it in two dimensions.
 * In other words, using Coxeter notation for Coxeter reflection groups may be really the best and clearest way to refer to those groups.
 * But I agree with GuenterRote's comment that it is essential to state exactly what defines the kind of group that is being listed — and which 4-dimensional point groups are being included or excluded, if the list is not complete.

History
"2018 N. W. Johnson Geometries and Transformations, Chapter 11,12,13, Full polychoric groups, p. 249, duoprismatic groups p. 269"

p.269 just lists the wallpaper groups. In fact the term "duoprismatic" never appears in that book. The full symmetries of the regular polytopes have been known for decades. I find it exaggerated to list a monograph that summarizes this among the history. --GuenterRote (talk) 10:48, 19 March 2021 (UTC)

Mistake? Fixed.
"Icositetrachoric group – F4, [3,4,3], (...), order 1152, (Du Val #45 (O/T;O/T)*, Conway [O×O].23)"

In Conway & Smith [9], there is no [O×O].23. --GuenterRote (talk) 05:14, 27 December 2020 (UTC)


 * Excuse me, but how could we ever know that if Conway & Smith [9] is under copyright? Not everyone is capable of making revisions if the source is not publicly accessable without purchase or affiliation. Shadi1089 (talk) 20:37, 17 March 2021 (UTC)


 * I happen to have a library nearby that has the book. I think books are legitimate references in Wikipedia. (Any anyway, it was not I who wrote the article and put the reference there.) — Preceding unsigned comment added by GuenterRote (talk • contribs) 10:57, 19 March 2021 (UTC)

Conway's notation?
"and John Conway (2003).[9] Conway's notation"

The reference [9] is a book by Conway and Smith. Why is it not called Conway and Smith's notation?

What are "ionic subgroups"?

 * Well, this is certainly a humorous way to post a "What is...?" question. Creating an entirely new subject header without actually writing anything. Not even I could have achieved such a feat. Shadi1089 (talk) 20:47, 17 March 2021 (UTC)

Possible typo
I am not an expert, but I suspect that the the "Order" column in the "Chiral subgroups" section may have some errors. In particular, the last two lines in the "Polyhedral prismatic groups" give the order of those direct subgroups as 96 and 240, the same as the corresponding full groups. I suspect that those two orders should be 48 and 120.

LyleRamshaw (talk) 00:10, 23 February 2017 (UTC)


 * There are definitely a few errors in the article, but no one has taken the time to make revisions. I would like to see this article get better attention and/or a more concise and readable format. Shadi1089 (talk) 04:14, 24 December 2020 (UTC)

I agree. fixed--GuenterRote (talk) 03:55, 27 December 2020 (UTC)

Organization
I am new to this area, but this seems to be a bit of a mess. Certainly, there is a lot of valuable material (which I appreciate!), but I don't see a proper organization. It is already not clear what the second sentence has to do with the first sentence.

For example in the table. What are the ranges of p and q in the last two lines? Obviously the next-to-last line is a special case of the last line. Where is BC2 x I2(p) for example? Is BC2 regarded as a special case of I2(4)? Then why is 2BC2 listed as a special case? Are the lines intended to be a classification into disjoint cases?

(Also, where do these names come from. I have seen alternate names for Coxeter groups that have only one letter, not like BC4)

188.106.190.173 (talk) 10:24, 30 November 2014 (UTC) Günter Rote


 * I've been using BC4 because the B4=C4=I2(4) for reflective groups, unlike Dynkin diagrams with unequal root lengths. And yes, any p,q are possible. I just included a few smaller cases first for examples. My current goal is to develop some visualizations for these groups, like for 3D polyhedral group. Tom Ruen (talk) 17:24, 30 November 2014 (UTC)


 * It would be in this article's best interest to have a clearer organisation. As it is right now it is not clear which values of p,q produce the crystallographic point groups in four dimensions. Furthermore, the lists of polychoral point groups are very cluttered and difficult to read. This article mentions crystallographic point groups, but a concise list is nowhere to be found in this article. Shadi1089 (talk) 21:34, 23 December 2020 (UTC)

Unusual terminology
It is beyond idiotic to use — and promote — terminology ("polychora", "pentachora" and their derived forms) that is extraordinarily uncommon among researchers studying polytopes, on the grounds that one professional mathematician (Norman Johnson) and one amateur mathematician (George Olshevsky) "advocated" their use during their lifetimes.

Incomplete table
I recently accessed this page, wondering whether there is a point group in 4 dimensions whose structure, as an abstract group, is $$S_5\times C_2$$. After looking through the big table that appears early on this page, I falsely concluded that there is no such group. In fact, there is such a group, with Coxeter notation $$3,3,3$$. It appears in the figure at the top-right of the page; and it is discussed as the "extended pentachoric group", about halfway down the page. But I was misled by its absence from that big table. When someone reorganizes this page, they might want to keep my experience in mind. LyleRamshaw (talk) 19:09, 21 January 2024 (UTC)